Testing of Hypothesis : Students t test

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25. Consider the following hypothesis test:
H :µ &#8805; 45
º
H :µ < 45
A sample of 36 is used. Identity the p-value and state your conclusion for each of the following sample results. Use a = .01
a. _
x = 44 and s = 5.2

b. _
x = 43 and s = 4.6

c. _ = 46 and s = 5.0
x

Answer

The test Statistic is given by

Rejection criteria: Reject the null hypothesis, if the calculated value of t is less than the critical value of t with n-1 d.f.
Or if the p value is less than the significance level 0.01
The critical value = -2.4377
Given that n = 36

27. The Employment and Training Administration reported the U.S. mean unemployment insurance benefit of $238 per week. A researcher in the state of Virginia anticipated that sample data would show evidence that the mean weekly unemployment insurance benefit in Virginia was below the national level.
A. Develop appropriate hypotheses such that rejection of H will support the researcher's contention º

B. For a sample of 100 individuals, the sample mean weekly unemployment insurance benefit was $231 with a sample standard deviation of $80. What is the p-value.